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AaronChen · 2023年05月02日

既然第一笔年金支付是在第十三年，为什么不可以当做一个20-13=7年的年金算出第十三年的PV，然后根据第十三年的PV算出第一年的PV

  1. CFA I
  2. Quantitative

NO.PZ2015120604000013

问题如下：

An annuity of $2,000 per year will be received for twenty years. The first payment is to be received at the end of thirteenth years. Assume the discount rate is 7% over next years, calculate the today's present value of the annuity

选项：

A.

$8,792.

B.

$9,408.

C.

$10,066.

解释：

B is correct.

  1. Calculate the PV of annuity at the end of the twentieth years : N = 20; I/Y = 7; PMT = -2,000; FV = 0; CPT PV = 21,188.03. ;
  2. Calculate the PV today: N = 12; PMT = 0; FV = -21,188.03; I/Y = 7; CPT PV = 9,407.74.

13~20年的年金：N = 7; I/Y = 7%; PMT = 2000; FV = 0. 求出PV

1~13没有支付年金，将第十三年的PV当做FV，从而用FV和PV的公式求出第一年的PV

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1 个答案

星星_品职助教 · 2023年05月02日

同学你好，

这道题是13年才开始首笔付款的20年年金（... will be received for twenty years），也就是从13时点首笔付款开始连续付20笔PMT。不是一个20年但前7年没付款的年金。

所以第一步求PV的过程里N是20，也就是答案解析里的第一步思路。

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